Warm up the whole body, then earn the push-up.
Keep your core braced the whole walk so your hips never sag.
Adding a push-up to the walkout turns a mobility drill into a full upper-body primer. The walk out to plank sets your chest up to press from a strong, braced position, with the triceps and shoulders assisting the push exactly as they will in every press that follows. It is the warm-up move to reach for before chest or push sessions, because it rehearses the pressing pattern while it loosens you up.
Drop your knees for the push-up and keep the rest of the movement identical. The walkout still does its job, and you can graduate to full push-ups as you get stronger.
Enough to feel warm and moving well, not enough to fatigue your chest before the real work. It is a primer, so stop well short of grinding reps.
Before push days, yes, because the push-up rehearses the exact pressing pattern you are about to load. On lower-body days, the plain walkout does everything you need without taxing your chest.
